*Manuscript JCLEC-MO: a Java suite for solving many-objective optimization engineering problems Aurora Ram´ırez, Jos´eRa´ulRomero∗, Carlos Garc´ıa-Mart´ınez, Sebasti´an Ventura Department of Computer Science and Numerical Analysis, University of C´ordoba, 14071 C´ordoba Spain Abstract Although metaheuristics have been widely recognized as efficient techniques to solve real-world optimization problems, implementing them from scratch remains difficult for domain-specific experts without programming skills. In this scenario, metaheuristic optimization frameworks are a practical alterna- tive as they provide a variety of algorithms composed of customized elements, as well as experimental support. Recently, many engineering problems re- quire to optimize multiple or even many objectives, increasing the interest in appropriate metaheuristic algorithms and frameworks that might integrate new specific requirements while maintaining the generality and reusability principles they were conceived for. Based on this idea, this paper introduces JCLEC-MO, a Java framework for both multi- and many-objective opti- mization that enables engineers to apply, or adapt, a great number of multi- objective algorithms with little coding effort. A case study is developed and explained to show how JCLEC-MO can be used to address many-objective engineering problems, often requiring the inclusion of domain-specific ele- ments, and to analyze experimental outcomes by means of conveniently con- nected R utilities. Keywords: Metaheuristic optimization framework, multi-objective optimization, many-objective optimization, evolutionary algorithm, particle ∗Corresponding author. Tel.: +34 957 21 26 60 Email addresses: [email protected] (Aurora Ram´ırez), [email protected]. (Jos´e Ra´ulRomero), [email protected] (Carlos Garc´ıa-Mart´ınez), [email protected] (Sebasti´an Ventura) Preprint submitted to Engineering Applications of Artificial Intelligence October 5, 2018 swarm optimization 1. Introduction Optimization problems frequently appear in the engineering field, but their characteristics make the application of mathematical methods not al- ways feasible (Singh, 2016). Hence, the use of efficient search methods has ex- 5 perienced a significant growth in the last years, specially for those engineering problems where there are multiple objectives that require to be simultane- ously optimized (Marler and Arora, 2004). A recurrent situation in engineer- ing is the need of jointly optimizing energy consumption, cost or time, among others. All these factors constitute a paramount concern to the expert, and 10 represent conflicting objectives, each one having a deep impact on the fi- nal solution (Marler and Arora, 2004). Initially applied to single-objective problems, metaheuristics like evolutionary algorithms (EAs) have been suc- cessfully applied to the resolution of multi-objective problems (MOPs) in engineering, such as the design of efficient transport systems (Dom´ınguez 15 et al., 2014) or safe civil structures (Zavala et al., 2014). The presence of a large number of objectives has been recently pointed out as an intrinsic characteristic of engineering problems (Singh, 2016), for which the currently applied techniques might not be efficient enough. It is noteworthy that other communities are also demanding novel techniques to 20 face increasingly complex problems, what has led to the appearance of the many-objective optimization approach (von L¨ucken et al., 2014; Li et al., 2015). This variant of the more general multi-objective optimization (MOO) is specifically devoted to overcome the limits of existing algorithms when problems having 4 or more objectives, known as many-objective problems 25 (MaOPs), have to be faced. Even though each metaheuristic follows different principles to conduct the search, their adaptation to deal with either MOPs or MaOPs share some similarities, such as the presence of new diversity preservation mechanisms or the use of indicators (Li et al., 2015; Mishra et al., 2015). The resulting many-objective algorithms have proven successful in 30 the engineering field too (Li and Hu, 2014; L´opez-Jaimes and Coello Coello, 2014; Cheng et al., 2017), where specialized software tools have begun to appear (Hadka et al., 2015). In fact, the availability of software suites is one of the factors that most in- fluences engineers when selecting a solution or algorithm (Marler and Arora, 2 35 2004), as they can greatly reduce coding efforts and even provide some guid- ance to engineers. In this context, metaheuristic optimization frameworks (MOFs) (Parejo et al., 2012) seem to go one step further, as they may in- tegrate environments not only providing a collection of algorithms or code templates, but also other general utilities to properly configure them and 40 analyze outputs. MOFs are modular and adaptable in different ways, and should enable the introduction of specific domain knowledge and constraints in terms of the representation and evaluation of solutions (L´opez-Jaimes and Coello Coello, 2014; Singh, 2016). Focusing on the resolution of MOPs, these suites are expected to keep the 45 principles of multi-objective optimization by making the appropriate adap- tations for their components to deal with multiple objectives. At the same time, MOFs still need to consider aspects like efficiency, utility and integra- bility if a broad industrial adoption is sought. Among the currently available alternatives, there are some specialized frameworks like jMetal (Durillo and 50 Nebro, 2011) and MOEA Framework (Hadka, 2017), whose main strength lies on a more extensive catalog of recent algorithms. Besides, other general- purpose MOFs like ECJ (White, 2012), HeuristicLab (Elyasaf and Sipper, 2014) or JCLEC (Ventura et al., 2008) benefit other aspects like their ease of use and greater availability of components to represent and modify the 55 solutions are their key advantages. A mix of both alternatives would enable to take advantage of reusabil- ity, maturity and the reduction of the learning curve promoted by general- purpose components, whereas specialization might bring the suite closer to comply with current requirements of industry. At this point, JCLEC has 60 been reported as a competitive tool due to its large number of customiz- able components, which can be combined to solve user-defined optimization problems (Parejo et al., 2012). In addition, JCLEC can be easily integrated with other systems because of its regular use of standards like XML. Its core elements are defined at a high level of abstraction, providing the required 65 flexibility to build new functionalities on top of a stable platform. Therefore, JCLEC has become an interesting baseline MOF to be extended to adopt different metaheuristics for the resolution of both MOPs and MaOPs within an industrial environment. To this end, this paper presents JCLEC-MO, an extensible framework 70 providing suitable search elements and techniques for multi- and many- objective optimization. The preliminary architecture (Ram´ırezet al., 2015), only focused on multi-objective evolutionary algorithms (MOEAs), has been 3 refined and significantly evolved to include new types of algorithms and sup- port for other metaheuristics. As a result, JCLEC-MO provides generic 75 metaheuristic models that have been conveniently adapted to the precepts of MOO, and still preserves the valuable characteristics of a general-purpose so- lution. The conceptual algorithmic model proposed to achieve independence and a significant scalability is a distinctive characteristic of JCLEC-MO. It is also competitive in terms of the available catalog of algorithms, mecha- 80 nisms to assess their performance and reporting capabilities. A case study shows how this suite enables the resolution of a many-objective engineering problem, thus serving to illustrate how user-defined components should be conceived and how the returned solutions could be analyzed, e.g. by using R functionalities. 85 The rest of the paper is organized as follows. Section 2 provides an essen- tial background on metaheuristics for multi- and many-objective optimiza- tion and MOFs. Existing frameworks for solving multi-objective problems are analyzed in Section 3. Section 4 presents the design criteria and architecture of JCLEC-MO. A more detailed description of the software functionalities 90 and its modular organization is provided in Section 5. Then, Section 6 devel- ops an illustrative case study to show the applicability and use of JCLEC-MO as a supportive tool for engineers. A discussion of the benefits of JCLEC- MO compared to other available MOFs is presented in Section 7 and, finally, conclusions are outlined in Section 8. 95 2. Background Metaheuristics, just like evolutionary algorithms (Eiben and Smith, 2015) and particle swarm optimization (PSO) (Poli et al., 2007), are well-known techniques to address optimization problems due to their efficiency and inde- pendence of the problem formulation. Based on the principles of natural evo- 100 lution, EAs manage a set of candidate solutions (population of individuals) that are iteratively selected, recombined and mutated to gradually produce improved solutions. In PSO, each particle represents a potential solution that changes its position and velocity influenced by the rest of particles. Other bio- inspired metaheuristics imitate the behavior of other forms of living beings, 105 such as ants or bees, when looking for resources like food sources (Boussa¨ıd et al., 2013). These paradigms were promptly adapted to deal with problems having more